1. ## word problem help!

So, I'm not really sure how to even start on this word problem. Could someone help and walk me through it? Thanks a lot.

The number of inches that a young redwood tree grows per year can be modeled by f(x)=−0.05x2+x+1, where x represents annual rainfall in inches, and f(x) is the tree's annual growth, in inches. How many inches of rainfall produces the maximum annual growth in the tree?

2. Originally Posted by bananamash
So, I'm not really sure how to even start on this word problem. Could someone help and walk me through it? Thanks a lot.

The number of inches that a young redwood tree grows per year can be modeled by f(x)=−0.05x2+x+1, where x represents annual rainfall in inches, and f(x) is the tree's annual growth, in inches. How many inches of rainfall produces the maximum annual growth in the tree?
You need to find the maximum of f(x) and solve it for x.
Do you know how to find it?
Either you find the zeros of f(x): x1 and x2 and you calculate x(max) = (x1+x2)/2 or you find the derivative of f(x) [but I'm not sure if you have ever heard about the derivative yet]

Using "Completing the square" is another possible solution.

3. Spoiler: